Calculation of $\pi$ to 100,000 decimals

Authors:
Daniel Shanks and John W. Wrench

Journal:
Math. Comp. **16** (1962), 76-99

MSC:
Primary 65.99

DOI:
https://doi.org/10.1090/S0025-5718-1962-0136051-9

MathSciNet review:
0136051

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References | Similar Articles | Additional Information

- George W. Reitwiesner,
*An ENIAC determination of $\pi $ and $e$ to more than 2000 decimal places*, Math. Tables Aids Comput.**4**(1950), 11â€“15. MR**37597**, DOI https://doi.org/10.1090/S0025-5718-1950-0037597-6 - S. C. Nicholson and J. Jeenel,
*Some comments on a NORC computation of $\pi $*, Math. Tables Aids Comput.**9**(1955), 162â€“164. MR**75672**, DOI https://doi.org/10.1090/S0025-5718-1955-0075672-5
G. E. Felton, â€śElectronic computers and mathematicians,â€ť - FranĂ§ois Genuys,
*Dix mille dĂ©cimales de $\pi $*, Chiffres**1**(1958), 17â€“22 (French). MR**94928**
This unpublished value of $\pi$ to 16167D was computed on an IBM 704 system at the Commissariat Ă lâ€™Energie Atomique in Paris, by means of the program of Genuys.
C. StĂ¶rmer, â€śSur lâ€™application de la thĂ©orie des nombres entiers complexes Ă la solution en nombres rationnels, ${x_1}, {x_2}, \cdot \cdot \cdot ,{x_n}$, ${c_1}, {c_2}, \cdot \cdot \cdot , {c_n}$, - S. Ramanujan,
*Modular equations and approximations to $\pi $ [Quart. J. Math. 45 (1914), 350â€“372]*, Collected papers of Srinivasa Ramanujan, AMS Chelsea Publ., Providence, RI, 2000, pp. 23â€“39. MR**2280849**, DOI https://doi.org/10.1016/s0164-1212%2800%2900033-9

*Abbreviated Proceedings of the Oxford Mathematical Conference for Schoolteachers and Industrialists at Trinity College, Oxford, April 8-18, 1957*, p. 12-17, footnote p. 12-53. This published result is correct to only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished. For a detailed account of calculations of $\pi$ see J. W. Wrench, Jr., â€śThe evolution of extended decimal approximations to $\pi$,â€ť

*The Mathematics Teacher*, v. 53, 1960, p. 644-650.

*k*de lâ€™Ă©quation ${c_1}$ $\operatorname {arctg} {x_1} + {c_2}$ $\operatorname {arctg} {x_2} + \cdot \cdot \cdot + {c_n}$ $\operatorname {arctg} {x_n} = {k\pi }/{4}$,â€ť

*Archiv for Mathematik og Naturvidenskab*, v. 19, 1896, p. 69. C. F. Gauss,

*Werke*, GĂ¶ttingen, 1863; 2nd ed., 1876, v. 2, p. 499-502.

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Article copyright:
© Copyright 1962
American Mathematical Society